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Beran M.J. — Statistical Continuum Theories
Beran M.J. — Statistical Continuum Theories

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Название: Statistical Continuum Theories

Автор: Beran M.J.

Аннотация:

This book is primarily intended to acquaint the reader with the problems we face when we formulate a continuum problem from a statistical point of view. In the early chapters I emphasize what is meant by the solution to a statistical continuum problem and in the later chapters we present the techniques of solution that have been used in four separate fields. It is hoped that the book will be suitable for second- or third-year graduate students in engineering and physics and for research workers in the variety of disciplines that use statistical formulations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 424

Добавлена в каталог: 09.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Analytic signal      44 158
Angular diameter, stars      174
Angular diameter, two-point objects      151
Axially symmetric tensors      138 225 230 252
Blackbody radiation      176
Boltzmann's equation      406
Capillary models      264 275
Coherence, blackbody radiation      176
Coherence, coherent and incoherent fields      149
Coherence, far-field approximation      169
Coherence, functional solution      85
Coherence, functions      44 145 155
Coherence, governing equations      158
Coherence, Green's functions      85 163
Coherence, quasi-monochromatic radiation      147 166
Coherence, radiation from a plane finite surface      165
Coherence, star, measurement of angular diameter      174
Coherence, visibility      144
Conditional probability      21
Conductivity      see "Permittivity"
Cumulant neglect hypothesis      117 121 361
Darcy's law      262
Decay of correlation functions      172 231 234 240 353 368
Diagrammatic techniques      388
dielectric constant      see "Permittivity"
Dilute suspensions      200 247
Direct interaction equations      369 398
Dispersion in porous media      268 288
Dispersion in porous media, effect of molecular diffusion      304
Displacement field      see "Permittivity"
Eddy "size"      344
Eddy viscosity      318 323 360 404
Effective constants, bounds      131 141 245 246 288
Effective constants, definitions      126 131 184 191
Effective constants, determination from perturbation solutions      229 235 240
Effective constants, dilute suspensions      200 247
Effective constants, n-phase materials      197
Effective constants, self-consistent approximation      199
Effective constants, simple models      192
Elasticity, effective constants      182 212 240
Elasticity, fluctuations      240
Elasticity, statistical moment equations      236
Electric field fluctuations      229 232 235
Ensemble, concept of      18
Ensemble, variational principle      128
Ergodic hypothesis      41
Expectations      30
Functionals      56
Functionals, characteristic      71
Functionals, continuity      57
Functionals, delta      63 79 90 410
Functionals, differentiation      62
Functionals, governing equations, harmonic oscillator      75
Functionals, governing equations, Maxwell's equations      81
Functionals, governing equations, Navier — Stokes equations      87 400
Functionals, integration      67
Functionals, linear      59
Functionals, probability density      70
Functionals, Taylor series      60
Gaussian processes      36 49 72 179 271 362 389 402 412
Geometry, heterogeneous media      202
Geometry, porous media      258
Harmonic oscillator, functional equations      75
Harmonic oscillator, introduction      6
Harmonic oscillator, moment equations      96 104
Harmonic oscillator, other treatments      117 125 382
Heterogeneous media, effective constants      see "Effective constants"
Heterogeneous media, geometry      202
Heterogeneous media, statistical moment equations      215
Heterogeneous media, statistical moment equations, elastic case      236
Heterogeneous media, statistical moment equations, electrostatic case      216
Heterogeneous media, statistical moment equations, electrostatic case, scalar permittivity      230 232
Heterogeneous media, statistical moment equations, electrostatic case, tensor permittivity      225 250
Heterogeneous media, variational principles      126 241
Hilbert transform      43 146
Homogeneity, heterogeneous media      112 128 182 211
Homogeneity, turbulence      337
Hydraulic radius      265
inclusion      186 199 200 247
Incoherent radiation      149
Isotropic, direct interaction equations      378
Isotropic, equations for turbulence      343 349
Isotropic, radiation field      176
Isotropic, tensors      177 218 338
Karhunen — Loeve theorem      55
Kolmogorov's hypothesis      355 382 402
Kozeny equation      266 277
Lambertian source      175
Liouville's equation      92 403
Maxwell's equations      81 155
Mixing lengths      318 323 330
Moments, definitions      32 35
Moments, different type      94
Moments, equations      93 104 158 215 334
Moments, Fourier transforms of      112 343
Moments, solutions      116
n-phase materials      197 199
Navier — Stokes equations      87 101 109 263 316 370 385 406
Permeability      262 278 283
Permittivity, bounds      131 141 245
Permittivity, cumulant neglect hypothesis      121
Permittivity, effective constants      210 229 232 235
Permittivity, functional equation      82
Permittivity, moment equations      99 105 216
Permittivity, one-dimensional problem      10 193
Permittivity, perturbation solution      118 222
Permittivity, variational principles, Brown, Hashin, Shtrikman-type      132 247
Permittivity, variational principles, standard      126 241
Perturbation theory      114 118 222 385
Poisson point model      207
Polarization      132
Polycrystal      189 217 224 250
Porosity      259 263
Porous media, Darcy's law      262
Porous media, description      258
Porous media, dispersion      268 288
Porous media, flow through, correlation lengths      260
Porous media, Green's function      278 281
Porous media, permeability      262 278 286
Porous media, random capillary model      275
Porous media, spherical arrangement      259 273
Porous media, variational principle      283
Power spectra      44
Power spectra, smoothing procedure      48
Probability theory, axiomatization      18
Probability theory, characteristic functionals      71
Probability theory, characteristic functions      31
Probability theory, characterization of a two-phase medium      204
Probability theory, conditional probability      21
Probability theory, convergence      33 53
Probability theory, correlation functions      35 43
Probability theory, density functionals      70
Probability theory, density functions      22
Probability theory, description of porous media      258
Probability theory, distribution functions      26
Probability theory, ergodic hypothesis      41
Probability theory, gaussian processes      49 72
Probability theory, mathematical expectations      30
Probability theory, moments      32 37
Probability theory, power spectra      43
Probability theory, semiinvariants      34
Probability theory, stationary processes      38
Probability theory, transformation of variables      28
Propagation of radiation through random media      85 118 154 180 400
Quasi-monochromatic radiation      147 166
Radiation      83 162
Reynolds' equation      316
Reynolds' number      267 303 313 327 357
Self-consistent approximation      199
Semiinvariants      34 122 124
Similarity hypothesis      331 384
Stability      317
Star, measurement of angular diameter      174
Stationary processes      38 156
Strain fluctuations      240
Stress fluctuations      240
Symmetric materials      245 246 256
Taylor pipe dispersion problem      289
Taylor series      60 95
Tchebycheff's inequality      53
Tortuosity      266
Turbulence, analogy to quantum field theory      408
Turbulence, cumulant neglect hypothesis      361 381
Turbulence, direct interaction equations      369 398
Turbulence, eddy "size"      344
Turbulence, eddy viscosity      318 323 360
Turbulence, energy transfer      354 381
Turbulence, experiments in channel flow      327
Turbulence, final period of decay      350 402
Turbulence, functional approaches      400
Turbulence, Heisenberg's theory      358
Turbulence, homogeneous      337
Turbulence, homogeneous and isotropic      338
Turbulence, inertial range      357
Turbulence, Kolmogorov's hypothesis      355
Turbulence, Lagrangian fields      370 383 385
Turbulence, lateral correlation function      342
Turbulence, Loitsianski's invariant      367
Turbulence, longitudinal correlation function      342
Turbulence, mixing lengths      318 323 330
Turbulence, Reynolds' equation      316
Turbulence, Reynolds' number      267 303 313 327 357
Turbulence, Reynolds' studies      312
Turbulence, shear flow      312 412
Turbulence, similarity hypothesis      323 331 384
Turbulence, stability      317
Turbulence, statistical moment equations      101 109 334
Turbulence, vorticity      366
Turbulence, Wyld's perturbation procedure      385
Turbulent diffusion      125 314 335 363 404
Van Cittert — Zernike theorem      174
Variational principles      126
Variational principles, heterogeneous media      241 247
Variational principles, porous media      283
Viscosity, eddy      318 323 360 404
Viscosity, kinematic      319
Visibility      144
Volume fractions      185
Wiener — Khinchin theorem      46
Young's interference experiment      143
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